1. Field of the Invention
The present invention relates to a system for removing ambiguity from ambiguous information and knowledge of control, pattern recognition, decision making and so on. Particularly, the present invention concerns a defuzzification system comprising a consequent defined by fuzzy singletons, the range width and shift of a centroid value being variable depending on the purpose of control.
2. Description of the Related Art
FIG. 3 schematically illustrates a simplified fuzzy inference system having a consequent defined by fuzzy singletons. In general, the fuzzy inference uses a rule of inference which is described by a so-called "IF-THEN rule". The "IF" part is called the "antecedent" while the "THEN" part is called the "consequent". In the fuzzy inference, the descriptions other than "IF" and "THEN" parts are expressed, as a fuzzy set, by the membership characteristic function to provide an inference on ambiguous knowledge.
When the fuzzy set in the descriptions other than the "consequent" part is replaced by fuzzy singletons, it is called a "simplified process". Such a "simplified process" is increasingly being used in various fields including control and so on since the number of calculation steps are greatly reduced.
The algorithm in the simplified fuzzy process will be described with reference to FIG. 3. When an element x is inputted into the system, the operational result due to the membership characteristic function described in the antecedent is calculated for each rule. The calculated value is called "degree of satisfaction" from which an inferential result for that rule is determined in the inputted element x. Since the consequent in the simplified process is defined by fuzzy singletons, the degree of satisfaction itself in the antecedent directly becomes the grade of the inferential result.
Subsequently, the grades determined from a plurality of rules are unified, for example, by MAX (maximum) operation. In many realistic cases, it is required to output a single decided value from the unified inferential result. Such an operation is called "defuzzification" and is generally carried out by determining the weighted average of the unified inferential result or center of gravity. The calculation is represented by the following equation: ##EQU1## where i represents each of the singletons defining the consequent; n is the total number of fuzzy singletons; W.sub.i expresses the element of each fuzzy singleton; and .mu..sub.i is the grade of each fuzzy singleton. The numerator in the equation (1) is the weight adding value of each inferential grade while the denominator is a simple adding value. The centroid value thus determined is a decided output in the fuzzy inference.
If the fuzzy inference is defined by hardware, the range width and value of an input to a subsequent device depends on the subsequent circuit and device. Therefore, it may be required that the output range width of the centroid value is expanded and contracted and also that the output of the centroid value is shifted.
In the fuzzy control, it is further required to determine the output range width of the consequent into a proper width. If the output range width of the consequent is larger than the proper width, the sensitivity of the system to variations in input is increased, but an over-operation may be raised. If the output range width of the consequent is smaller than the proper width, the system is not sensitive to variations in input, but the amount of operation decreases to avoid the over-operation.
It is therefore required that the output range width of the consequent can be expanded or contracted to meet an object or purpose to be controlled.
It is therefore an object of the present invention to provide simplified fuzzy inference hardware comprising means for varying the output range width of the centroid value and shifting the centroid value depending on the input range width from subsequent circuits and devices and means for varying the scaling or controlled variable of the consequent depending on the purpose of fuzzy control.